Neural Nets and Symbolic Reasoning 

Second Semester 2012/2013, 6 EC, Block A

Lecturer: PD Dr. Reinhard Blutner
, University of Amsterdam

Lectures: Monday 9-11 in A1.10; Wednesday 15-17 in B0.201.

Office Hours: by appointment
Science Park 107 (Nikhef), Room F1.40


Parallel distributed processing is transforming the field of cognitive science. In this course, basic insides of connectionism (neural networks) and classical cognitivism (symbol manipulation) are compared, both from a practical perspective and from the point of view of modern philosophy of mind. Discussing the proper treatment of connectionism, the course debates common misunderstandings, and it claims that the controversy between connectionism and symbolism can be resolved by a unified theory of cognition – one that assigns the proper roles to symbolic computation and numerical neural computation.

(1) Classical cognition, (2) Neural nets and parallel distributed processing, (3) The connectionist-symbolist and emergentist-nativist debates, (4) Connectionism and the mind body problem (5) Towards a unifying theory.


This course will be graded based on


Part  A

Please tell me the topic of your essay/presentation before week 6 (March 10) per email!

Part B

Possible topics for projects/essays

  1. What is systematicity?
    Tim van Gelder and Lars Niklasson: Classicalism and Cognitive Architecture
    Blutner, Hendriks, de Hoop, Schwartz: When Compositionality Fails to Predict Systematicity

  2. Modelling conceptual combination
    Edward E. Smith, Daniel N.Osherson, Lance J. Rips, and Margaret Keane: Combining Prototypes: A Selective Modification Model
    If prototype theory is to be extended to composite concepts, principles of conceptual composition must be supplied. This is the concern of the present paper. In particular, we will focus on adjective-noun conjunctions such as striped apple and not very red fruit, and specify how prototypes for such conjunctions can be composed from prototypes for their constituents. While the specifics of our claims apply to only adjective-noun compounds, some of the broader principles we espouse may also characterize noun-noun compounds such as dog house.

    Barry Devereux & Fintan Costello: Modelling the Interpretation and Interpretation Ease of Noun-Noun Compounds Using a Relation Space Approach to Compound Meaning
    How do people interpret noun-noun compounds such as gas tank or penguin movie? In this paper, we present a computational model of conceptual combination. Our model of conceptual combination introduces a new method of representing the meaning of compounds: the relations used to interpret compounds are represented as points or vectors in a high-dimensional relation space. Such a representational framework has many advantages over other approaches. Firstly, the highdimensionality of the space provides a detailed description of the compound’s meaning; each of the space’s dimensions represents a semantically distinct way in which compound meanings can differ from each other. Secondly, representation of compound meanings in a space allows us to use a distance metric to measure how similar of different pairs of compound meanings are to each other. We conducted a corpus study, generating vectors in this relation space representing the meanings of a large, representative set of familiar compounds. A computational model of compound interpretation that uses these vectors as a database from which to derive new relation vectors for new compounds is presented.

  3. Relating and unifying connectionist networks and propositional logic
    Gadi Pinkas (1995). Reasoning, connectionist nonmonotonicity and learning in networks that capture propositional knowledge. [1,6 MB!]
    Reinhard Blutner (2005): Neural Networks, Penalty Logic and Optimality Theory

  4. Symbolic knowledge extraction from trained neural networks
    A.S. d’Avila Garcez, K. Broda, & D.M. Gabbay (2001). Symbolic knowledge extraction from trained neural networks: A sound approach.
    Although neural networks have shown very good performance in many application domains, one of their main drawbacks lies in the incapacity to provide an explanation for the underlying reasoning mechanisms. The “explanation capability” of neural networks can be achieved by the extraction of symbolic knowledge. In this paper, we present a new method of extraction that captures nonmonotonic rules encoded in the network, and prove that such a method is sound.   
  5. Natural deduction in connectionist systems
    William Bechtel (1994): Natural Deduction in Connectionist Systems
    The relation between logic and thought has long been controversial, but has recently influenced theorizing about the nature of mental processes in cognitive science. One prominent tradition argues that to explain the systematicity of thought we must posit syntactically structured representations inside the cognitive system which can be operated upon by structure sensitive rules similar to those employed in systems of natural deduction. I have argued elsewhere that the systematicity of human thought might better be explained as resulting from the fact that we have learned natural languages which are themselves syntactically structured. According to this view, symbols of natural language are external to the cognitive processing system and what the cognitive system must learn to do is produce and comprehend such symbols. In this paper I pursue that idea by arguing that ability in natural deduction itself may rely on pattern recognition abilities that enable us to operate on external symbols rather than encodings of rules that might be applied to internal representations. To support this suggestion, I present a series of experiments with connectionist networks that have been trained to construct simple natural deductions in sentential logic. These networks not only succeed in reconstructing the derivations on which they have been trained, but in constructing new derivations that are only similar to the ones on which they have been trained.

  6. Modelling logical inferences: Wason's selection task and connectionism
    Steve J. Hanson,  Jacqueline P. Leighton , & Michael R.W. Dawson: A parallel distributed processing model of Wason’s selection task
    Three parallel distributed processing (PDP) networks were trained to generate the ‘p’, the ‘p and not-q’ and the ‘p and q’ responses, respectively, to the conditional rule used in Wason’s selection task.  Afterward, each trained network was analyzed for the algorithm it developed to learn the desired response to the task. Analyses of each network’s solution to the task suggested a ‘specialized’ algorithm that focused on card location. For example, if the desired response to the task was found at card 1, then a specific set of hidden units detected the response. In addition, we did not find support that selecting the ‘p’ and ‘q’ response is less difficult than selecting the ‘p’ and ‘not-q’ response. Human studies of the selection task usually find that participants fail to generate the latter response, whereas most easily generate the former. We discuss how our findings can be used to (a) extend our understanding of selection task performance, (b) understand existing algorithmic theories of selection task performance, and (c) generate new avenues of study of the selection task. 

  7. Infinite RAAM: A principled connectionist substrate for cognitive modelling
    Simon Levy and Jordan Pollack (2001): Infinite RAAM
    Unification-based approaches have come to play an important role in both theoretical and applied modeling of cognitive processes, most notably natural language. Attempts to model such processes using neural networks have met with some success, but have faced serious hurdles caused by the limitations of standard connectionist coding schemes. As a contribution to this effort, this paper presents recent work in Infinite RAAM (IRAAM), a new connectionist unification model. Based on a fusion of recurrent neural networks with fractal geometry, IRAAM allows us to understand the behavior of these networks as dynamical systems. Using a logical programming language as our modeling domain, we show how this dynamical-systems approach solves many of the problems faced by earlier connectionist models, supporting unification over arbitrarily large sets of recursive expressions. We conclude that IRAAM can provide a principled connectionist substrate for unification in a variety of cognitive modeling domains.

  8. Encoding nested relational structures in fixed width vector representations.
    Tony A. Plate
    (2000): Analogy retrieval and processing with distributed vector representations
    Holographic Reduced Representations (HRRs) are a method for encoding nested relational structures in fixed width vector representations. HRRs encode relational structures as vector representations in such a way that the superficial similarity of the vectors reflects both superficial and structural similarity of the relational structures. HRRs also support a number of operations that could be very useful in psychological models of human analogy processing: fast estimation of superficial and structural similarity via a vector dot-product; finding corresponding objects in two structures; and chunking of vector representations. Although similarity assessment and discovery of corresponding objects both theoretically take exponential time to perform fully and accurately, with HRRs one can obtain approximate solutions in constant time. The accuracy of these operations with HRRs mirrors patterns of human performance on analog retrieval and processing tasks.
  9. New solutions to the binding problem
    Abeles, Heyon, Lehmann (2004): Modeling Compositionality by Dynamic Binding of Synfire Chains
    This paper examines the feasibility of manifesting compositionality by a system of synfire chains. Compositionality is the ability to construct mental representations, hierarchically, in terms of parts and their relations. We show that synfire chains may synchronize their waves when a few orderly cross links are available.We propose that synchronization among synfire chains can be used for binding component into a whole. Such synchronization is shown both for detailed simulations, and by numerical analysis of the propagation of a wave along a synfire chain. We show that global inhibition may prevent spurious synchronization among synfire chains. We further show that selecting which synfire chains may synchronize to which others may be improved by including inhibitory neurons in the synfire pools. Finally we show that in a hierarchical system of synfire chains, a part-binding problem may be resolved, and that such a system readily demonstrates the property of priming. We compare the properties of our system with the general requirements for neural networks that demonstrate compositionality.

    See also: van der Velde (2005): Neural blackboard architectures

  10. The role of symbolic grounding within embodied cognition / Grounding symbols with neural nets
    Michael L. Anderson: Embodied Cognition: A field guide
    Stevan Harnad: Grounding symbols in the analog world with neural nets -- A hybrid model (Target Article on Symbolism-Connectionism)
    Bruce J. MacLennan: Commentary on Harnad on Symbolism-Connectionism
    Stevan Harnad: Symbol Grounding and the Symbolic Theft Hypothesis

  11. Subsymbolic language processing using a central control network
    Risto Miikkulainen: Subsymbolic case-role analysis of sentences with embedded clauses
    A distributed neural network model called SPEC for processing sentences with recursive relative clauses is described. The model is based on separating the tasks of segmenting the input word sequence into clauses, forming the case-role representations, and keeping track of the recursive embeddings into different modules. The system needs to be trained only with the basic sentence constructs, and it generalizes not only to new instances of familiar relative clause structures, but to novel structures as well. SPEC exhibits plausible memory degradation as the depth of the center embeddings increases, its memory is primed by earlier constituents, and its performance is aided by semantic constraints between the constituents. The ability to process structure is largely due to a central executive network that monitors and controls the execution of the entire system. This way, in contrast to earlier subsymbolic systems, parsing is modelled as a controlled high-level process rather than one based on automatic reflex responses.

  12. Implicit learning
    Bert Timmermans & Axel Cleeremans: Rules vs. Statistics in Implicit Learning of Biconditional Grammars
    A significant part of everyday learning occurs incidentally — a process typically described as implicit learning. A central issue in this domain and others, such as language acquisition, is the extent to which performance depends on the acquisition and deployment of abstract rules. Shanks and colleagues [22], [11] have suggested (1) that discrimination between grammatical and ungrammatical instances of a biconditional grammar requires the acquisition and use of abstract rules, and (2) that training conditions — in particular whether instructions orient participants to identify the relevant rules or not — strongly influence the extent to which such rules will be learned. In this paper, we show (1) that a Simple Recurrent Network can in fact, under some conditions, learn a biconditional grammar, (2) that training conditions indeed influence learning in simple auto-associators networks and (3) that such networks can likewise learn about biconditional grammars, albeit to a lesser extent than human participants. These findings suggest that mastering biconditional grammars does not require the acquisition of abstract rules to the extent implied by Shanks and colleagues, and that performance on such material may in fact be based, at least in part, on simple associative learning mechanisms.
  13. Echo state machines

  14. Herbert Jaeger: Discovering multiscale dynamical features with hierarchical Echo State Networks: Many time series of practical relevance data have multi-scale characteristics. Prime examples are speech, texts, writing, or gestures. If one wishes to learn models of such systems, the models must be capable to represent dynamical features on different temporal and/or spatial scales. One natural approach to this end is hierarchical models, where higher processing layers are responsible for processing longer-range (slower, coarser) dynamical features of the input signal. This report introduces a hierarchical architecture where the core ingredient of each layer is an echo state network. In a bottom-up flow of information, throughout the architecture increasingly coarse features are extracted from the input signal. In a top-down flow of information, feature expectations are passed down. The architecture as a whole is trained on a one-step input prediction task by stochastic error gradient descent. The report presents a formal specification of these hierarchical systems and illustrates important aspects of its functioning in a case study with synthetic data.

  15. Conceptual spaces and compositionality
    Peter Gärdenford & Massimo Warglien: Semantics, conceptual spaces and the meeting of minds
    We present an account of semantics that is not construed as a mapping of language to the world, but mapping between individual meaning spaces. The meanings of linguistic entities are established via a “meeting of minds.” The concepts in the minds of communicating individuals are modeled as convex regions in conceptual spaces. We outline a mathematical framework based on fixpoints in continuous mappings between conceptual spaces that can be used to model such a semantics. If concepts are convex, it will in general be possible for the interactors to agree on a joint meaning even if they start out from different representational spaces. Furthermore, we show by some examples that the approach helps explaining the semantic processes involved in the composition of expressions.
  16. Automatic formation of topological maps
    Teuvo Kohonen: Self-organized foration of topologically correct feature maps. This work contains a theoretical study and computer simulations of a new self-organizing process. The principal discovery is that in a simple network of adaptive physical elements which receives signals from a primary event space, the signal representations are automatically mapped onto a set of output responses in such a way that the responses acquire the same topological order as that of the primary events. In other words, a principle has been discovered which facilitates the automatic formation of topologically correct maps of features of observable events. The basic self-organizing system is a one- or twodimensional array of processing units resembling a network of threshold-logic units, and characterized by short-range lateral feedback between neighbouring units. Several types of computer simulations are used to demonstrate the ordering process as well as the conditions under which it fails.
  17. Neural networks for simulating statistical models of language
    Yoshua Bengio, Réjean Ducharme, Pascal Vincent, and Christian Jauvin: A Neural Probabilistic Language Model
    Holger Schwenk, Daniel Dchelotte and Jean-Luc Gauvain: Continuous Space Language Models for Statistical Machine Translation
  18. Learning Pattern Recognition Through Quasi-Synchronization of Phase Oscillators
    Patrick Suppes et al.
    The idea that synchronized oscillations are important in cognitive tasks is receiving significant attention. In this view, single neurons are no longer elementary computational units. Rather, coherent oscillating groups of neurons are seen as nodes of networks performing cognitive tasks. From this assumption, we develop a model of stimulus-pattern learning and recognition. The three most salient features of our model are: 1) a new definition of synchronization; 2) demonstrated robustness in the presence of noise; and 3) pattern learning.
  19. Analogical inference, scheme induction and relational resoning
    John E. Hummel & Keith J. Holyoak: Relational Reasoning in a Neurally-plausible Cognitive Architecture: An Overview of the LISA Project.
    Human mental representations are both flexible and structure-sensitive—properties that jointly present challenging design requirements for a model of the cognitive architecture. LISA satisfies these requirements by representing relational roles and their fillers as patterns of activation distributed over a collection of semantic units (achieving flexibility) and binding these representations dynamically into propositional structures using synchrony of firing (achieving structure-sensitivity). The resulting representations serve as a natural basis for memory retrieval, analogical mapping, analogical inference and schema induction. In addition, the LISA architecture provides an integrated account of effortless “reflexive” forms of inference and more effortful “reflective” inference, serves as a natural basis for integrating generalized procedures for relational reasoning with modules for more specialized forms of reasoning (e.g., reasoning about objects in spatial arrays), provides an a priori account of the limitations of human working memory, and provides a natural platform for simulating the effects of various kinds of brain damage.

Books used to prepare the lecture

Practical Instructions: Tlearn


Tips for the installation of T-learn for Windows XP (thanks go to Dewi!)

1. Go to properties on the menu. It will load a box, click on the last "tab". You can open T-learn in a previous version of windows (98 will work), thus preventing it from crashing!

2.  When a new project is created, or an existing one is opened, if the path to the file is longer than a length of approx. 50 characters and/or contains spaces, the program crashes or closes unexpectedly, making it impossible to use. Please also note that this is very likely to be the case if the user runs Windows 2000 or XP, and the project files are on the desktop or the "My Documents folder" (absolute path would be similar to "C:\Documents and Settings\YourName\My Documents"). An easy solution to the problem is to only open/create project files for which the path is relatively small and contains no spaces (eg. c:\tlearn). I would recommend running the program (tlearn.exe) from a similar path as well.

Tips for setting the parameters (thanks go to Ben!)

learn.exe automatically sets the 'log error every' parameter to 100. The consequence of this is that the errors you will see are still relatively high and a 100 hidden node network hardly improves. Best, to set set this parameter to 1. The parameter is in training options and then more.

Related Websites